Casimir force between topological insulator slabs

Abstract

The Casimir force between two finite-thick topological insulator slabs and its dependence on the gap size between the slabs are investigated in detail. Two typical substrate materials including semi-infinite vacuum and silicon are used in the study, in which the Casimir force can always change from attractive to repulsive when the gap size decreases. The gap width at transition is a function of the slab thickness and also depends strongly on the electric permittivity and topological magnetoelectric polarizability of the slabs. In particular, in the absence of a substrate, this width increases with decreasing slab thickness and for thin slabs with large internal and external topological magnetoelectric polarizability the Casimir force is always repulsive where the surface topological magnetoelectric effect of the slabs plays a dominant role. In the presence of a semi-infinite silicon substrate, however, the attractive role of the silicon substrate becomes increasingly important, and thus the transition gap decreases with decreasing thickness of the slab. The characteristic features of the Casimir force may be detected experimentally through exploring its gradient with a certain dynamical method.